Hybrid Reasoning About Relative Position and Orientation of Objects and Navigating Agents Using Answer Set Programming

We study reasoning about relative position, orientation and distance of moving objects in 2D space. We first construct a new hybrid calculus HOPA by augmenting qualitative distance and quantitative constraints into Oriented Point Relation Algebra (OPRA). Then we develop a framework for consistency checking and reasoning with HOPA using Answer Set Programming. This framework can also explain the source of inconsistency, infer new knowledge and generate a layout of objects and their orientation in the discrete space. The framework is capable of reasoning with (un)certain, heterogenous and presumed information. We evaluate efficiency and scalability of our method by computational experiments, and illustrate its applications with sample scenarios from robotic perception and marine navigation.